The Big Bang
To the Editor:
As a working cosmologist, I enjoyed David Berlinski’s poetic description of the Big Bang [“Was There a Big Bang?,” February]. I also share much of his healthy skepticism about some of the more speculative extensions of the theory.
But there are several errors and omissions in his article that, separately, are innocuous enough, but, taken together, leave an impression vastly different from the one I have as an active worker in the field. For me, as for many of my colleagues, this is the golden age of cosmology. Data are flowing in at an unprecedented rate. We believe we know the answers to some very important questions, though there remain unsolved problems that may well be addressed in the coming decade. Mr. Berlinski suggests that the basis for our glee is faltering. I perceive otherwise: every pillar of modern cosmology has received new and exciting support within the last few years.
For example, Mr. Berlinski incorrectly claims that helium is the only element formed in the Big Bang; the rest, he says, “wait patiently for the stars to be born.” There is one omission here and one error. The omission is that Big Bang theory predicts how much helium there should be in the universe today, a little less than 25 percent, and, in fact, this is precisely the percentage of helium that has been observed. The error is that, contrary to what Mr. Berlinski claims, other light elements are also produced in the Big Bang, albeit in much smaller quantities than helium. These abundances have also been predicted and also agree with observations. For example, in the last few years—using the Keck telescope in Hawaii—astronomers have detected deuterium in the oldest clouds ever observed. The amount of deuterium in these clouds conforms to expected levels.
My own area of research is the radiation left over from the Big Bang, and here Mr. Berlinski omits several crucial facts. First, the spectrum of this radiation has been measured with extraordinary precision. If the radiation came from the earliest moments of the universe, we would expect the spectrum to have a black-body shape, since it should have completely thermalized—and recent measurements confirm that it has this shape to an accuracy of one part in 10,000. It is hard to conceive of any mechanism other than the Big Bang that would have produced such a precise black-body spectrum.
Mr. Berlinski’s error on this topic is even more telling. He claims that “looking at the sky in every direction, cosmologists have discovered that the cosmic background radiation (CBR) has the same temperature, to an accuracy of one part in 100,000.” But in the last few years, there have been dozens of detections of deviations from this uniformity. We expect these deviations, because, as Mr. Berlinski notes, the universe today is not smooth and homogeneous. Thus, early on, the universe had to be lumpy. Our theories predict how lumpy the CBR should be, and they agree remarkably well with the new observations.
It is important to separate this part of cosmology from the more speculative part where, as Mr. Berlinski notes, “the equations of general relativity fall silent.” He questions the value of any theories proposed in this latter area. To me it is hard to say that none of these will pay off in the end. Nevertheless, no matter what side one takes on the issue of pre-Big Bang speculations, it is hard to see how things could be going better for the Big Bang.
The cosmologists I know are not stupid and, for the most part, not arrogant. There are no young cosmologists working on the 30-year-old criticisms of Big Bang theory by Halton Arp and I.E. Segal that Mr. Berlinski cites. The reason is simple. We are attracted to the Big Bang not because we are blind sheep too ignorant to examine the evidence. Rather, we are convinced by the vast evidence that supports the basic picture. And we are excited, very excited, by the prospect of testing our theories of how structure formed in the universe with the ever-increasing data we are now receiving.
To the Editor:
David Berlinski shows serious ignorance when he says: “There are three kinds of universe to consider, and innumerably many species within each type. Those that are open and forever gushing into the void are called hyperbolic.” In making this statement, Mr. Berlinski seems unaware that in the presence of a cosmological constant, the terms open and closed have two distinct usages. The terms may be used to characterize the topology, i.e., the geometric structure, of a model and simultaneously and independently the model’s dynamic behavior. The term hyperbolic is used invariably in the former context and means a curved model of infinite spatial extent. When the terms open and closed are used to characterize the model’s dynamic behavior they signify, respectively, a model that will expand forever and one that will expand to a maximum size and then contract to its original state. The possibility that the universe may be permanently static was ruled out by the British astronomer and physicist Arthur Eddington, who demonstrated that such models are unstable.
Mr. Berlinski’s ignorance of these concepts is further highlighted by his statement that “the universe may be one that occupies the Euclidean space . . . balanced precariously but balanced forever between a knife’s edge of expansion and contraction.” But in fact there are cosmological models that are both stable and expanding.
Mr. Berlinski’s discussion of the discovery of the CBR is also seriously skewed:
It is often said . . . that the physicists Arno Penzias and Robert Wilson observed the remnants of the Big Bang when in 1962 they detected, by means of a hum in their equipment, a signal in the night sky they could not explain. This is not quite correct. What Penzias and Wilson observed was simply the same irritating and ineradicable noise that has been a feature of every electrical appliance I have ever owned. What theoreticians like Robert Dicke inferred was something else: a connection between that cackle and the cosmic background radiation released in the universe after the era of recombination.
Firstly, it was neither a hum nor a cackle that Penzias and Wilson discovered, it was a hiss. And Robert Dicke was not a theoretician but an experimentalist of considerable competence who was also knowledgeable about the theory of background radiation. Although Penzias and Wilson were at a loss to understand the hiss, Dicke immediately suggested it was the CBR. At that very time Dicke and his coworkers were setting up an experiment to look for that radiation. When Dicke learned of Penzias’s and Wilson’s discovery, he told his group, “We’ve been scooped.” Finally, radiation of almost the same temperature as that discovered by Penzias and Wilson had been predicted on the basis of a Big Bang hypothesis some twenty years earlier by George Gamow, Robert Hermann, and Roger Alpher.
The steady-state hypothesis in which “nothing ever begins and nothing ever quite ends” could not accommodate the existence of the CBR and consequently was abandoned by most cosmologists. The existence of the CBR was considered decisive in determining the rejection of the Bondi-Gold-Hoyle steady-state theory in favor of the Big Bang.
Mr. Berlinski’s ignorance of the relation of mathematics and physics is exemplified by his characterization of the Hawking-Penrose singularity theorems:
Hawking and Penrose proved something [but] what they demonstrated remains within the gerbil wheel of mathematics; any additional inference requires a connection that the mathematics is not in a position to provide.
This is completely wrong; the singularity theorems provide precisely the connection between the mathematics of the physical source terms (i.e., mass and radiation) of the Einstein equations and the curved, dynamic space in which and with which they interact. The theorems imply that, traveling directly backward in time, one will encounter a point beyond which one cannot proceed. That (singular) point is approached with a simultaneous approach to infinite density of the sources. These theorems, then, though they do not prove the existence of the Big Bang, are perfectly compatible with it.
Where does the work of Halton Arp and I.E. Segal stand in all this? Arp is an observational astronomer of recognized competence, but his interpretations have failed to gain acceptance. Much of the controversy involves statistical analyses of presumed relationships between galaxies and what Arp calls “associated” quasars, i.e., quasars that he insists are very close nearby. These quasars have redshifts that, according to Hubbies law, imply that they are much farther away than the galaxies in question. Because there has yet to be found a satisfactory mechanism other than recessional motion, i.e., the Doppler effect, to explain the redshift, most cosmologists do not have Arp’s confidence that these associations are real.
Segal faces an entirely different problem in gaining acceptance of his thesis. He attacks the Hubble relationship on the basis of statistical studies. Such attacks are not unique; the scientific literature contains a steady stream of them. None has survived careful examination. Much of cosmology is based on statistical studies of sets of observational data extremely difficult to obtain and more difficult to interpret. A major part of Arp’s and Segal’s work is the interpretation of these data. This is a slippery area requiring the most careful and circumspect treatment.
Emeritus Professor, Physics
New York City
To the Editor:
Almost two years ago, David Berlinski bashed Darwinian evolution [“The Deniable Darwin,” June 1996] without letting us know what kind of creationism should replace it. Now he attacks cosmological evolution. Because there are grave doubts about the redshift as a measure of the receding velocity of galaxies, he concludes that there is equal doubt that the universe is expanding, and thus no sound reason to assume the universe originated in a Big Bang. Presumably the universe Mr. Berlinski prefers is static.
Please, Mr. Berlinski, do not be shy about your hidden agenda. Clear the air. What are your theological assumptions? Are you defending a Jewish or a Christian Creator—or neither, or both? We do not yet know where you stand with respect to religious faith. How about telling us?
To the Editor:
David Berlinski is mistaken to criticize cosmologists who believe there was a Big Bang for speculating what might have caused it. While it is correct to say that science must eventually end in mystery, one never knows beforehand exactly how far science can go until it reaches its limits. Many times, what seemed beyond scientific understanding later proved to be amenable to it. And speculation is often a key first step in the scientific process.
It is, rather, creation scientists who should be criticized because they refuse to speculate about what might have caused the creation event they believe occurred, and which they dogmatically insist can never be understood.
Mr. Berlinski’s concluding point is that science and myth should not be mixed. But if it is wrong for some cosmologists to go beyond scientific speculation and make a religion out of science, creation scientists are equally wrong to make a science based on myth. Mixing the two is as bad for religion as it is for science. I wish that Mr. Berlinski would take the powerful critical powers he has applied to Darwin and the Big Bang theory and turn them on creation science.
To the Editor:
What a shame that David Berlinski’s intriguing deliberations are seriously marred by speculation about the concept of creation. It is not just that he regards the idea of creation as “incoherent,” but that he does so on the basis of a staggeringly silly or crudely question-begging “argument” by the 3rd-century Chinese sage Kuo Hsiang. Here, as presented by Mr. Berlinski, are the putatively golden words:
I venture to ask . . . whether the Creator is or is not. If He is not, how can he create things? And if He is, then (being one of these things) He is incapable (without self-creation) of creating the mass of bodily forms.
Mr. Berlinski then goes on to urge that the argument should not be thought wrong just because it is “simple.” Of course not; elegance or simplicity is often a desirable feature of an argument. Unfortunately, however, it is of little help here. Consider: central to all versions of theism is the thesis that what is ultimately real is divine; moreover, what is divine is, ipso facto, perfect or unlimited in all respects. However, anything that requires creation in order to exist is, if only in that regard, metaphysically defective. Accordingly, it is axiomatic to theism that the ultimately real is uncreated, and, moreover, possesses, by virtue of its perfection, the power to create those finite things that require creation in order to exist.
While I doubt it very strongly, there may be some argument just waiting to be discovered or developed that establishes that theistic views of reality are incoherent. Clearly, however, that argument is not to be found among the observations of Kuo Hsiang.
Saint Louis, Missouri
To the Editor:
My only reservation about David Berlinski’s otherwise sharp analysis is the way he conflates ancient Hebrew cosmology with other mythical accounts of creation. His wider point, I think, is valid: that there is a fundamental distinction between mythical and scientific world views. But that does not obviate differences between Hebrew and, for example, Babylonian cosmology.
According to the biblical scholar Yehezkel Kaufmann, monotheism was part of Israel’s patrimony from the outset. This means that the Bible’s account of creation is fundamentally different from all others known to historians of religion. For in all other (pagan) myths, the gods are born. But the God of Israel has no pedigree and fathers no generations.
Mr. Berlinski sees a connection between Bible and Babylon here, between primordial Apsu the Begetter having sexual congress with Mummu-Tiamet (who in Babylonian myth bore the worlds as a result of this mating) and the Hebrew Creator God. For Mr. Berlinski, this shows that all myths, biblical and pagan, posit a Great Cause as the origin of universal being. Kaufmann, however, would see the emergence of the world in Babylonian myth as a natural and thus unwilled process, whereas the God of Genesis willed the universe into being, including and especially the fundamental contrasts of light and darkness, good and evil, night and day, male and female, etc. of Genesis 1.
To my mind, the charter for all theistic versions of cosmology can be found in a short essay of Thomas Aquinas entitled “On the Eternity of the World,” in which he argued that while the Bible reveals that God happened to have brought the world into being at a moment in time, it is nonetheless perfectly consonant with God’s power to have created the world from all eternity.
Now, in my opinion, exegesis can no longer maintain with Aquinas that Genesis reveals the beginning of the world in time, since the opening verse in Hebrew can also be translated: “At that time when God began to apportion heaven and earth, the earth was [already] formless and void.” This might not be the best option for the translator, but its very possibility no longer makes it imperative to insist that the Bible reveals a beginning to the universe in time.
Ironically enough, as Mr. Berlinski points out, most popular accounts of the Big Bang leave the general public with the impression that the universe did have a kind of beginning. Hence, perhaps, the rush of theists to embrace this development, laboring as they do under two mistaken impressions, that both the Bible and Big Bang theory reveal a beginning to the universe.
Edward T. Oakes, S.J.
To the Editor:
Although I am largely unschooled in the sciences, and probably have no right to form an opinion, I have nevertheless been rather skeptical of the Big Bang. My discomfort has arisen from the inclusion of a “singularity” (something not governed by the laws of physics) as one of its necessary components. The dependence of Big Bang theory on an event that science cannot explain has seemed to me, in essence, hardly different from an affirmation or belief that God created the universe, that is, more an article of faith than of fact. My skepticism, however, was tempered by the observed expansion of the universe, Hubble’s law, which is, of course, suggestive of a prior powerful propulsive occurrence.
Now we are informed by David Berlinski that Hubble’s law may not hold the status of even a simple ordinance. Mr. Berlinski has also pared away, with razorlike yet accessible logic, every other significant support for the Big Bang. In so doing, he has indicted what must be a large part of the scientific community for embracing or for failing to abandon that which can be regarded, in the absence of further evidence, as only the merest of conjectures.
Is this lapse on the part of those supposedly dedicated to the scientific method of small consequence because it is limited to cosmology, a subject inherently speculative, or is Mr. Berlinski implying that science and scientists in general must be given careful scrutiny? If the latter, how does the public go about that task? Perhaps a part of the answer lies with people like Mr. Berlinski who will bring to our attention what we need to know.
Martin T. Goldblum
Beverly Hills, California
David Berlinski writes:
I am not at all certain that Scott Dodelson and I have a substantial disagreement, but there are points that require clarification.
The golden age of cosmology? In a certain sense, this is no doubt true. Technical advances in the interpretation and analysis of cosmological data have for the first time made it possible seriously to address a number of quantitative issues that until recently have been beyond the grasp of the scientific community. If in my article I seemed to suggest otherwise, that was not my intention. The question I raised was whether Big Bang cosmology coheres theoretically and empirically in a fashion that would warrant its promotion to a governing secular myth. My conclusion was that it does not.
Mr. Dodelson argues that Big Bang cosmology not only predicts the formation of helium but places a reasonably tight quantitative bound on helium’s presence in the universe, one confirmed by observation. I do not disagree, but there is a subtle distortion of emphasis in his claim. The theory of nucleosynthesis was pioneered in the 1940’s by George Gamow, Roger Alpher, and Robert Hermann, who realized that with the distance between stellar objects collapsing, cosmology would sooner or later become a branch of nuclear physics. The formation of helium is thus a prediction of nuclear physics; its direct connection to Big Bang cosmology requires a further series of inferences, many of which, to my mind, are not entirely tenable.
Mr. Dodelson correctly observes that I did not discuss the formation of other light elements, and thus gave the impression that except for helium, all others are formed in solar interiors. I accept the criticism and apologize for an incomplete formulation. But so long as we are discussing the matter, it is worth noting that the predicted quantitative bounds for other light elements are not entirely in accord with prevailing theories of nucleosynthesis, a fact routinely observed with some satisfaction by steady-state cosmologists.
Mr. Dodelson’s most substantial comments concern cosmic background radiation (CBR). If he thinks I failed to observe its black-body shape, he has misread me; I referred specifically to blackbody radiation in my exposition (pp. 29-30) of the standard version of hot Big Bang cosmology.
Mr. Dodelson is correct that in recent years there have been dozens of small deviations in the uniformity of observed temperature. These deviations lie at the heart of the theory of galaxy formation, and for obvious reasons: a profoundly inhomogeneous universe, such as the one we inhabit, cannot easily be derived from an entirely homogeneous background. But the deviations are also too close to the margin of experimental error for complete comfort. The fact remains that the CBR is astonishingly uniform, and this fact continues to be an ad-hoc assumption in standard Big Bang cosmology, one among others that various theories of inflation are meant to explain.
Mr. Dodelson is wrong in suggesting that the prediction of the CBR is a unique triumph of Big Bang cosmology. In this regard, he might consult I.E. Segal’s paper, “Radiation in the Einstein Universe and the Cosmic Background” (Physical Review D, vol. 28, number 10, November 1983).
Finally, I did not say, nor did I mean to imply, that cosmologists are either stupid or arrogant. As everyone knows, they are very smart. But as in so many other areas of intellectual inquiry, cosmologists tend to move as a herd of individuals. Dissenting voices are ignored; they rarely receive funding.
In referring to “the 30-year-old criticisms of Arp and Segal,” Mr. Dodelson inadvertently betrays the very instinct to which I am calling attention. Segal’s criticisms are of 30 years’ standing, but they are not 30 years out of date. Segal has published a continuous record of criticism; his most recent paper, dated January 3,1998, “Cosmological Implications of a Large Complete Quasar Sample,” is scheduled for publication in the Proceedings of the National Academy of Science (April 28, 1998). The same point holds for Halton Arp, whose criticisms are entirely contemporary. The indifference of the cosmological community to their research is shameful.
The distinguished COSmologist Alex Harvey has allowed his indignation to obscure his good sense.
The terms “open” and “closed” do have a meaning in point-set topology; and within general topology, one talks of open balls and the open-ball topology. The issue is utterly irrelevant. I was talking of cosmological models within the context of the solutions to the field equations of general relativity known as FL cosmology (for the work of Aleksandr Friedmann and Georges Lemaître in the 1920’s); and also, as I made unmistakably clear, within a context where the cosmological constant is set to zero.
Under these conditions and the conditions of homogeneity and isotropy, there are three classes of solutions within FL cosmology, and only three. One is closed, one flat, and one hyperbolic—hyperbolic in the understood sense that the universe is roughly the four-dimensional analogue to a portion of a saddleback. The proof may be found in any well-known text on general relativity—for example, on pp. 96-105 of Robert M. Wald’s General Relativity.
The claim that a static universe must be unstable is simply not true. Arthur Eddington, in his paper, “On the Instability of Einstein’s Spheroidal Worlds” (Monthly Notices of the Royal Astronomical Society, vol. 90,1930, pp. 668-78), made his argument with respect to a particular world model.
A few other matters of business. Robert Dicke is known in the physics community as a theoretician, not as an experimentalist. Here is how he is listed in the latest edition of the Encyclopedia Britannica: “U.S. physicist noted for his theoretical work in cosmology and investigations centering on the general theory of relativity” (emphasis added). And Mr. Harvey, I am quite certain, has heard of the “Brans-Dicke gravitational theory.”
Whether Penzias and Wilson heard a noise, a hum, a cackle, or a hiss is a question that I am prepared to cede. Let us say they heard a hiss. What then?
The issue of the singularity theorems is far more complicated than Mr. Harvey is prepared to admit. As I took pains to stress in my article, cosmologists have been unable to describe the singularities of Einstein’s theory in a way that is mathematically natural, plausible, elegant, and persuasive. They still cannot. Mr. Harvey is convinced that the original Hawking-Penrose theorem arose from very plausible physical assumptions, but this is a mistake. Theorems 1 and 2 of Stephen Hawking’s and G.F. Ellis’s The Large Scale Structure of Space-Time contain complex mathematical assumptions about the structure of a certain differential manifold. Their proofs are long, clumsy, and, as some mathematicians have maliciously suggested, perhaps fully comprehensible only to their graduate students. Still, there is no question that under a number of problematic conditions, singularities figure in general relativity. I never said otherwise.
General relativity is completely a mathematical theory, one containing a number of physical parameters. In this respect it is no different from any other theory within physics. Such theories confront the physical universe as an idealization; but very often the idealization, however plausible, is simply wrong.
The angles of a triangle in the real world sum to more or less 180 degrees. More or less: there are inevitable errors of measurement. In the case of local Euclidean geometry, we accept those errors as small, and move on. But the singularity theorems confront us with something entirely different: predictions that to this point have made no physical sense. Thus, Hawking and Ellis very sensibly conclude, after eliminating a number of other possibilities, that “. . . one can regard a singularity as a point where the Einstein equations (and presumably the other known laws of physics) break down.” This was Einstein’s conclusion, too.
Physicists cannot have it both ways. They cannot say, as does Joseph Silk, that terms like infinite density are absolutely unacceptable as physical descriptions, and then argue that general relativity predicts their physical existence. The matter is one of logic, not mathematics. If Mr. Harvey is in a position to extend the field equations so that in the context of singularities they make reasonable physical sense, I wish him well. So far, no one has done so, virtually the entire community of cosmologists agreeing with Einstein that under singular conditions, general relativity fails as a physical theory.
If the field equations (and everything else) break down within a singularity, and if the concept of an initial singularity is incoherent, as, given our present understanding, it surely is, what precisely remains of the Big Bang hypothesis other than the putative fact that the universe is expanding? To say that the conclusions of the singularity theorems are consistent with the hypothesis of the Big Bang is only to say that something we do not understand is compatible with something we cannot describe.
Mr. Harvey seriously and unfairly misrepresents the true situation with respect to Arp’s and Segal’s criticisms. Halton Arp was not given a respectful hearing for his heterodox views; his interpretation of quasars was subjected to statistical criticism of almost flamboyant incompetence. The facts are on record in his own very interesting book, Quasars, Redshifts, and Commentaries. I have carefully studied Segal’s 30-year record of criticism. As I suggested in my reply to Scott Dodelson, I believe his standards of statistical and mathematical sophistication are of a different order entirely from those of his critics.
It is easy to say, because it is true, that statistical cosmological inferences are difficult to make. They are. But has it ever occurred to Alex Harvey that if so, there is reason to be very skeptical of positive statistical inferences, and very attentive to consistent, reproducible, and objective negative ones?
I am simply baffled by Martin Gardner’s insistence that I have a hidden agenda. I wrote neither of my COMMENTARY essays to advance any theological assumptions whatsoever. I swear it.
As for Les Brunswick’s concern, I have not undertaken to discuss creation science because I do not know what it is and have in any case no interest or talent for theology.
Mr. Brunswick is, of course, correct in asserting that it is sheer foolishness to set limits to scientific inquiry, and correct again in urging scientists to speculate freely. Who could disagree? But physics in particular, like science in general, is also a social institution bound by particular constraints, the most notable of which is to maintain a disciplined distinction between metaphysical speculation and rigorous physical reasoning. When this distinction is blurred under conditions in which physicists say anything that pops into their heads, physics is diminished.
To turn to Robert Oakes, the argument offered by Kao Hsiang strikes me as far more subtle than it does him. In one respect, indeed, Kao Hsiang was not only correct but prescient. If the goal of a rational explanation of the universe is to provide a complete account of creation from a central set of principles, then introducing a set of principles whose own truth cannot be demonstrated from those principles means, in effect, that the complete goal of rational inquiry cannot be met. This is part of the burden of the well-known theorems of Tarski and Gödel. (I discuss the issue more fully in “The End of Materialist Science,” Forbes ASAP, December 1996.) But I do not understand Mr. Oakes’s assertion that “. . . anything that requires creation in order to exist is, if only in that regard, metaphysically defective.” Why so?
I am glad that Edward T. Oakes agrees with me that the common interpretation of Big Bang cosmology as pointing to a universe finite in temporal origin is not coherent, philosophically or physically. But I also would not wish to be misunderstood. It is entirely possible that the physical evidence on hand will point inexorably toward a Big Bang. It is only in the light of the present depth of our theories that to think so suggests confrontation with a miracle, not a doctrine of physics. There is a difference, one that it is important to respect. Father Oakes’s other, theological comments I am unable (or unwilling) to address.
Finally, Martin T Goldblum raises an issue of profound importance within a secular culture. Although science as an institution is said to be uniquely self-critical, this is plainly true in only the most limited sense. The simple and dangerous fact is that science as an institution is largely uncritical, the more so in disciplines like evolutionary biology and cosmology that have profound social and moral implications.
Within particular scientific cultures, certain figures do command critical respect. In physics one thinks of the valuable role played recently by the late Richard Feynman; and within the larger context of 20th-century physics, Wolfgang Pauli’s snort of intellectual indignation was as crucial as his very significant positive contributions to physics itself. No one on the contemporary scene is in a position to play these roles.
But what role is the public to play in the assessment of scientific structures? In the case of evolutionary biology of the sort championed by Daniel Dennett or Richard Dawkins, or evolutionary psychology of the sort popularized by Steven Pinker, the answer is obvious: criticism is within the grasp of anyone who has read ten good books. In the case of cosmology, things are different. A difficult body of mathematics stands between the skeptical amateur and the theories he is asked to evaluate. There is no help for it: the mathematics and the physics must be learned, and not everyone has the time or the taste. But what is disturbing and disheartening is that our culture has produced very few scientific critics of competence willing to take on the task. The problem is one of education, to be sure, but it is also a problem of taboos that have been put in place by the scientific community itself.